I want to make sure I am doing this problem right!

Question

The marginal cost when producing widgets is $11 per widget. It costs $1150 to produce 100 widgets. Find the cost function. Find the fixed cost. Assume that widgets are priced at $12 per widget. Find the revenue function. Find the proft function. Find the breakeven point. Find the profit if we produce and sell 100 widgets.

I started like this: y= 11x + b and then did 100= 11(1150) to find the linear function. Is that right?

For the second part, I got x-12550 as the profit function. Is that right even if it is negative?

Answer 1

There is a mistake in your cost function. The cost of making 100 widgets is $1150. That should be in the place of the y variable. You were correct to put 11 by the x and to have an unknown b. That unknown b is the fixed cost. The 100 widgets is the x variable.

So it should look like this:

1150 = 11(100) + b

1150 = 1100 + b

50 = b

So the cost function is C(x) = 11x + 50.

The revenue function is easier. Since it is a flat price per widget, it is the price times the number of widgets, or R(x) = 12x.

The profit function P(x) is R(x) - C(x), which is P(x) = 12x - (11x + 50), or P(x) = x - 50..

Then if 100 widgets are produced and sold, the profit is P(100) = 100 - 50 = 50.